1. Vocabulary
corresponding angles
corresponding sides
congruent polygons

2. Geometric figures are congruent if they are the same size and shape
Geometric figures are congruent if they are the same size and shape. Corresponding angles and corresponding sides are in the same position in polygons with an equal number of sides.
Two polygons are congruent polygons if and only if their corresponding sides AND corresponding angles are congruent. Thus triangles that are the same size and shape are congruent.

5. To name a polygon, write the vertices in consecutive order
To name a polygon, write the vertices in consecutive order. For example, you can name polygon PQRS as QRSP or SRQP, but not as PRQS.
In a congruence statement, the order of the vertices indicates the corresponding parts.

6. Example 1: Naming Congruent Corresponding Parts
Given: ∆PQR  ∆STW
Identify all pairs of corresponding congruent parts.
Angles:
Sides:
If polygon LMNP  polygon EFGH, identify all pairs of corresponding congruent parts.
Angles:
Sides:

7. Example 2A: Using Corresponding Parts of Congruent Triangles
Given: ∆ABC  ∆DBC.
Find mD.

8. Example 2B: Using Corresponding Parts of Congruent Triangles
Given: ∆ABC  ∆DBC.
Find mABC

9. 5-4

10. Example 4: Applying the Third Angles Theorem
Find mK and mJ.

11. Example 3: Proving Triangles Congruent
Given: YWX and YWZ are right angles.
YW bisects XYZ. W is the midpoint of XZ. XY  YZ.
Prove: ∆XYW  ∆ZYW

12. Check It Out! Example 3
Given: AD bisects BE.
BE bisects AD.
AB  DE, A  D
Prove: ∆ABC  ∆DEC

13. Example 4: Engineering Application
The diagonal bars across a gate give it support. Since the angle measures and the lengths of the corresponding sides are the same, the triangles are congruent.
Given: PR and QT bisect each other.
PQS  RTS, QP  RT
Prove: ∆QPS  ∆TRS

14. Lesson Quiz
1. ∆ABC  ∆JKL and AB = 2x JK = 4x – 50. Find x and AB.
Given that polygon MNOP  polygon QRST, identify the congruent corresponding part.
2. NO  ____ T  ____
4. Given: C is the midpoint of BD and AE.
A  E, AB  ED
Prove: ∆ABC  ∆EDC